Problem was asked in 2012 cbse board exam. Problem from RS Aggarwal book problem number 3, exercise 17B, chapter volume and surface area of solid, page number 809
Deepak BoraNewbie
Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere
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The radii r1 = 6 cm,
r2 = 8 cm
r3 = 10 cm
Let the radius of the resulting sphere be R.
Volume of resulting sphere = Volume of three metallic spheres
[4/3]πR³ =([4/3]πr1³) + ([4/3]πr2³) + ([4/3]πr3³)
[4/3]πR³ =([4/3]π*6³) + ([4/3]π*8³) + ([4/3]π*10³)
[4/3]πR³ = [4/3]π ( 6³ + 8³ + 10³ )
R³ = 216 + 512 + 1000
R³ = 1728
∴ The radius of the resulting sphere is 12 cm